We use bond volatility, chain time, and dealer concentration as proxies for theories of the bid-ask spread in Section 4and for each proxy in turn, we calculate a predicted bid-ask spread as follows.
We estimate the regression
BAit =β0+β1pit+it (1)
whereBAitis the actual bid-ask spread of bondiat daytandpitis the specific proxy. The intercept in the regression should be zero: for example when we estimate equation (1) using bond return volatility as a proxy, inventory models predict that the bid-ask spread is zero if bond volatility is zero because there is no inventory risk. However, we include an intercept in the regression to allow for a fixed cost of market making.
We use the estimated regression parameters from equation (1) to calculate a predicted bid-ask spread as
same way as for the actual bid-ask spreads. For asymmetric information and dealer network theories, we calculate an implied bond bid-ask spread and use this directly when comparing to actual bid-ask spreads.
Note that the average actual bid-ask spreads in some tables are different from those in Table 3 because proxies may not exist for all observations of actual bid-ask spreads. In the tables, we therefore calculate an average actual bid-ask spread based on bid-ask spread observations for which we have values of the proxy and report the difference between average predicted and average actual bid-ask spreads in brackets.
Inventory
Standard models of inventory costs imply that bond bid-ask spreads increase with bond return volatility, since higher volatility implies larger fluctuations in the value of inventory. Table 9 shows annualized bond return volatility. Average bond volatility is 8.3% which is similar to the average bond volatility of 6.9% in Bao and Pan (2013). On average bond volatility increases in rating: volatility is 5.3% for Safe bonds increasing to 25.1% for C-rated bonds. We also see that average bond volatility increases in bond maturity from 5.2% for short maturities to 13.2% for long maturities. The positive relation between bond volatility and maturity is present in all rating categories except for the most risky C-rated, where the relation is flat. Likely, this is because prices of the most credit risky bonds depend primarily on the expected bond recovery value and for a given firm the expected recovery value is the same across bonds with different maturities.
Table10 shows the estimated parameters from equation (2). The estimate ˆβ0= 9.067 implies that the fixed cost of market making is 9.1 bps and ˆβ1 = 278.124 implies that a one percentage point increase in annualized bond volatility increases the bid-ask spread by 2.8 bps.
Table 11 shows predicted spreads when using bond volatility as the single explanatory vari-able for bond bid-ask spreads. Consistent with actual bid-ask spreads, average predicted spreads increase in bond maturity: the average implied (actual) spread for short-maturity bonds is 23.5 (19.8) bps and 45.9 (51.5) bps for long-maturity bonds.
Turning to the relation between bid-ask spreads and rating, Table 11 shows that there is a positive relation between predicted spreads and credit risk consistent with the actual relation. For example, the average predicted spread is 23.7 bps for Safe bonds and 78.8 bps for C-rated bonds.
However, predicted spreads are too high for speculative grade bonds and increasingly so for more credit risky bonds: average predicted spreads are higher than average actual spreads by 2.5 bps for BB-rated bonds, 11.7 bps for B-rated bonds, and 29.0 bps for C-rated bonds. For investment grade bonds, predicted spreads are broadly in line with actual spreads. The predicted spread for
long-maturity Safe bonds is 4.6 bps higher than for AA bonds, which is also in line with actual spreads.
Overall, variation in bond volatilities captures a large fraction of the variation in bid-ask spreads.
Search and bargaining
A major implication of search-based models is that there is a positive relation between bid-ask spreads and the time it takes dealers to intermediate bonds. Table10shows that this is indeed the case since the slope coefficient ˆβ1in the regression of bid-ask spreads on chain times is significantly positive.
Table9shows the average time it takes dealers to complete a round-trip intermediation chain.
Depending on bond maturity and rating, it takes dealers on average between 5.7 and 9.4 days to complete a chain. The table shows that it takes longer to intermediate long-maturity bonds compared to short-maturity bonds; for example it takes on average 7.7 days to intermediate long-maturity BBB bonds while the corresponding time is 6.4 days for short-long-maturity BBB bonds.
Across rating, chain time is lower for speculative grade bonds compared to investment grade bonds.
Table12shows average ask spreads predicted by chain times. Inconsistent with actual bid-ask spreads, there is little variation in predicted bid-bid-ask spreads both across rating and maturity, due to the modest variation in average chain times combined with a low loading on chain times.
Predicted bid-ask spreads range from 33.0 bps to 35.3 bps while actual bid-ask spreads range from 24.2 bps to 78.7 bps.
Turning to bargaining, we see in Table 9 that depending on rating and maturity the average dealer concentration is between 24.4% and 39.4%. To interpret this range, note that if there are three dealers with an equal market share, the Herfindahl-Hirschman index is 33.3%. The dealer concentration in the U.S. corporate market is substantially higher than in other OTC markets such as the markets for options, forwards, and interest rate swaps (seeCetorelli et al. (2007)).
Table 13 shows average predicted bid-ask spreads from bargaining. Predicted bid-ask spreads range from 32.4 bps to 35.6 bps, far below the actual range. The low range is, as is the case with search frictions, due to the low variation of dealer concentration combined with the low loading on dealer concentration.
Asymmetric information
If some investors have private information, dealers charge a positive bid-ask spread and obtain a positive profit from uninformed investors to offset losses arising from trading with the informed investors. In Appendix A we derive an unlevered bond bid-ask spread from the Merton (1974) model where we include asymmetric information as inCopeland and Galai(1983). In the model, the bond bid-ask spread is equal to the equity bid-ask spread times the sensitivity of bond returns to equity returns.
We calculate an equity bid-ask spread for each observation of the bond bid-ask spread and Table 9 shows average equity bid-ask spreads. Equity bid-ask spreads increase with credit risk, similar to the pattern in bond bid-ask spreads. However, the size of equity bid-ask spreads is smaller than in the bond market. For example, the average equity bid-ask spread for firms with Safe (BBB-rated) bonds is 6.9 (10.7) bps while the corresponding average bond spread in Table3 is 28.4 (36.3) bps. In models with asymmetric information, the bid-ask spread on equity is larger than the bid-ask spread on debt (see for exampleDang et al.(2015)).
Table 14 shows the bond bid-ask spread unlevered from the equity market. We see that unlevered bid-ask spreads are small, in particular for investment grade bonds. For example, the average predicted bond bid-ask spread for Safe bonds is only 0.1 bps, far from the average actual spread of 32.7 bps. The reason is that the sensitivity of bond returns to equity returns is too low to generate a significant unlevered bond bid-ask spread. As an example, the 10-year cumulative default rate for safe bonds is less than 0.23% and such small default rates have very modest effects on bond prices.7 In this case, private information about a safe bond issuer can have a sizeable effect on equity prices but will have almost no effect on bond prices. This in turn implies a sizeable equity bid-ask spread and a close-to-zero bond bid-ask spread.
Consistent with actual bond spreads, predicted bond spreads increase in maturity and rating, but the sizes of predicted spreads are substantially lower than actual spreads. Overall, the results show that asymmetric information only accounts for a minor fraction of bond bid-ask spreads.
Dealer network
Theories of dealer networks predict that how bonds are traded throughout the network of dealers is crucial for the bid-ask spread. As outlined earlier, we calculate an average markup for each dealer and then estimate a predicted bid-ask spread for each round-trip intermediation chain by adding the average markups of the dealers involved in the chain. If, for example, central dealers on average charge higher markups, predicted bid-ask spreads will be higher for chains involving
7SeeMoody’s(2018) Exhibition 35.
central dealers.
Table 15 presents predicted bid-ask spreads based on dealer network. We see that for long-maturity bonds, predicted spreads show a U-shaped pattern across rating consistent with actual bid-ask spreads: Safe bonds have substantially higher spreads than other investment grade bonds and for lower rated bonds there is a gradual increase in spreads. Thus, the dealer network is important in explaining the variation in bid-ask spreads for long-maturity bonds. For short-maturity bonds predicted spreads appear less consistent with actual spreads. In particular, average spreads predicted by the dealer network decrease in maturity which is in stark contrast to the increasing pattern in actual spreads. Overall, the results show that the dealer network is important for understanding spreads for long-maturity bonds across rating, while spreads across maturity remain unexplained by the dealer network.